I'm assuming villain is a fish based on non full stack and cold call of 3-bet. That's enough info to make him something more than an unknown imo. I'd be surprised to see anyone who raises 99-TT A8s etc here fold to a flop jam so think that if we're planning on not folding then flop is the place to get the rest in. 6, T, 9, Q, K, A turns happen frequently and defo hurt us by either improving him (yet it's still a guessing game when he ships, with this much already invested folding is bleh on many of these) or by making him reluctant to stack off with worse. I play the same but I'm not thrilled about it, nevertheless given villain is likely bad I'm not folding JJ here, this is the worst hand I'd felt though.